The quasi-static electromagnetic approximation for weakly conducting media

In a conducting medium dielectric charge and electric field decay with a time constant τR=ϵ/σ. In a weakly conducting medium, as e.g. glass or melamine-phenolic laminate in use in Resistive Plate Chambers (RPC), this time is about 10−3 s; so it is long compared to the time the charge cloud needs to move through the gap and to the time the signal needs to propagate through a dielectric to the electrode. A quasi-static theory to deal with transient phenomena in weakly conducting media has been developed in Haus and Melcher (Electromagnetic Fields and Energy, Prentice-Hall, Englewood Cliffs, NJ, 1989), Fano et al. (Electromagnetic Fields, Energy and Forces, Wiley, New York, 1963), Th. Heubrandtner (Dissertation, Technisch-Naturwissenschaftliche Fakultat, Technische Universitat Graz, 1999); it simplifies the analysis considerably since it requires only the solution of a scalar diffusion-type equations in place of the time-dependent Maxwell equations. This little known theory is applied to treat the generation of signals in simple models for chambers with such materials.